morphism of abstract shape

• 29 August 2025
• Mathematics,
• Process book,
• Learning,
• Sketchbook

🤖🌿
zzz
A presheaf goes backward,
but a copresheaf goes forward.
∃ means “there is,”
so the arrow goes one way.
∀ means “for all,” so it flips.
∈ points to Ω,
because Ω tells truth.
But if we flip,
Ω watches ∈ instead. 🌿🌊
zzz

🌰🌿
zzz
Prä-Sheaf: geht rückwärts
Co-Prä-Sheaf: geht vorwärt
∃ = “es gibt” 🐟
∀ = “für alle” 🌳
∈ zeigt auf Ω 🌊
Ω sagt Wahrheit
Flip: Ω schaut auf ∈
Mini-Satz: Fisch schwimmt,
BaumBoot segelt ⛵
zzz

a mini “math-poetry meditation”
nudges readers toward reflection,
not scroll addiction.
#accessibility #restorative
tiny ForestSea meditation:
engages reasoning + imagination 🐟⛵
slow attention, gentle dopamine 🌰
breaks compulsive loops 🌳
restorative micro-content:
playful, thoughtful, emoji-rich,
and accessible 🌊✨
Optional hashtag add-on:
#ForestSea #GentleContent
#NeuroFriendly #PlayfulLearning 🐬🌿

-- ForestSea mini arrow diagram 🌿🌊🐬  
inductive Object  
| Baum | Fisch | Boot  

inductive Morphism : Object → Object → Type  
| wächst  : Morphism Object.Baum Object.Baum  
| schwimmt: Morphism Object.Fisch Object.Boot  
| segelt  : Morphism Object.Boot Object.Boot  

-- Composition example: Baum∘Boot = Waldfahrt ⛵🌳  
def Waldfahrt := Morphism.wächst ∘ Morphism.segelt  

💡 Bright ∀

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